Related papers: A brief Introduction to Dispersion Relations and A…
These lecture notes give a pedagogical introduction to the use of dispersion relations in loop calculations. We first derive dispersion relations which allow us to recover the real part of a physical amplitude from the knowledge of its…
We give a pedagogical introduction to the founding ideas of dispersion relations in particle physics. Starting from elementary mechanical systems, we show how the physical principle of causality is closely related to the mathematical…
Dispersion relations are nonperturbative formulas that relate the ultraviolet and infrared behavior of an observable with wide-ranging applications applications in linear response theory, quantum field theory scattering amplitudes, and…
We derive dispersion relations for $K\to\pi\pi$ decay, using the Lehmann-Symanzik-Zimmermann formalism, which allows the analytic continuation of the amplitudes with respect to the momenta of the external particles. No off-shell…
These lectures aim to provide a basic introduction to dispersive methods and their modern applications to the phenomenology of the Standard Model at low energy. This approach exploits analyticity properties of Green functions and scattering…
Fractional calculus has been used to describe physical systems with complexity. Here, we show that a fractional calculus approach can restore or include complexity in any physical systems that can be described by partial differential…
The article surveys the known results and conjectures about the analytic properties of dispersion relations and Fermi surfaces for periodic equations of mathematical physics and their spectral incarnations.
We study field theories on the noncommutative Minkowski space with noncommuting time. The focus lies on dispersion relations in quantized interacting models in the Yang-Feldman formalism. In particular, we compute the two-point correlation…
I describe the methodology for the use of dispersion relations in connection with chiral perturbation theory. The conditions for matching the two formalisms are given at $O(E^2)$ and $O(E^4)$. The two have several complementary features, as…
We define a general notion of entropy in elementary, algebraic terms. Based on that, weak forms of a scalar product and a distance measure are derived. We give basic properties of these quantities, generalize the Cauchy-Schwarz inequality,…
Ab initio predictions of two-loop electroweak contributions to observables are increasingly essential for precision collider experiments, yet their evaluation remains very challenging. We connect recurrence techniques and dispersive method…
Generalized dispersion relations are discussed for unphysical particles, e.g. confined degrees of freedom that are not present in the physical spectra but can give rise to observable bound states. While in general the propagator of the…
Relating thermodynamic and kinetic properties is a conceptual challenge with many practical benefits. Here, based on first principles, we derive a rigorous inequality relating the entropy and the dynamic propagator of particle…
Starting from the Lorentzian inversion formula, we derive a dispersion relation which computes a four-point function in 1d CFTs as an integral over its double discontinuity. The crossing symmetric kernel of the integral is given explicitly…
The properties of the high energy behavior of the scattering amplitude of massive, neutral and spinless particles in higher dimensional field theories are investigated. The axiomatic formulation of Lehmann, Symanzik and Zimmermann is…
The kinematics of the two-scale relativity theory (new relativity) is revisited using a simplified approach. This approach allows us not only to derive the dispersion equation introduced earlier by Kowalski-Glikman, but to find an…
If the Electroweak Symmetry Breaking Sector turns out to be strongly interacting, the actively investigated effective theory for longitudinal gauge bosons plus Higgs can be efficiently extended to cover the regime of saturation of unitarity…
Taylor expansions of analytic functions are considered with respect to several points, allowing confluence of any of them. Cauchy-type formulas are given for coefficients and remainders in the expansions, and the regions of convergence are…
Taylor expansions of analytic functions are considered with respect to two points. Cauchy-type formulas are given for coefficients and remainders in the expansions, and the regions of convergence are indicated. It is explained how these…
We develop an analytic approach to the four-point crossing equation in CFT, for general spacetime dimension. In a unitary CFT, the crossing equation (for, say, the s- and t-channel expansions) can be thought of as a vector equation in an…